the polynomial (ax^3+3x^2-3)and (2x^3-5x+a) when divided by x-4 =1 leave the same remainder.find the value of a.
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The polynomials (ax^3 + 3x^2 - 3) and (2x^3 - 5x + a) when
divided by (x - 4) leaves the same reminder. What is
the value of a?
**
Using the Remainder Theorem which states: When a polynomial is divided by (x-a) the remainder=f(a).
..
Since given equations result in the same remainder when divided by (x-4), set f(4)1=f(4)2.
f(4)1=ax^3 + 3x^2 - 3=64a+48-3
f(4)2=2x^3 - 5x + a=128-20+a
64a+48-3=128-20+a
63a=63
a=1
Hope This Helps :)
divided by (x - 4) leaves the same reminder. What is
the value of a?
**
Using the Remainder Theorem which states: When a polynomial is divided by (x-a) the remainder=f(a).
..
Since given equations result in the same remainder when divided by (x-4), set f(4)1=f(4)2.
f(4)1=ax^3 + 3x^2 - 3=64a+48-3
f(4)2=2x^3 - 5x + a=128-20+a
64a+48-3=128-20+a
63a=63
a=1
Hope This Helps :)
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